Abstract

The traditional teaching approaches are generally teacher-directed and where students are taught in a manner that is conducive to sitting and listening. It is true that the traditional expectations and department philosophies often allow us to continue with the lecture-based model with some useful results as evident by the past accomplishments of many and this cannot be disputed as much. However it is often argued that the traditional approach may not provide students with valuable skills and indeed some even go as far as saying the traditional method leads to a student not retaining knowledge after exams - they have little or no recall of the body of knowledge learnt beyond the end of a semester, for example. The teaching of mathematics that is usually referred to or called non-traditional uses constructivist philosophy as its basis; this implicates strategies in which the individual is making sense of his or her universe. So the student is an active participant, which allows an individual to develop, construct or rediscover knowledge – a major goal that can be very time consuming process if taken literally for each student; alternately, there is also a philosophical position known as social constructivism; which suggests group work, language and discourse to be vital for learning in a cultural framework of the knowledge base; so the use of group work, discussion, and group solving problems in a cooperative manner lead to a discourse which is believed to be the most important part of learning process. It is argued that the non-traditional teaching is done using a problem solving approach; where the learner is the problem solver.

Typically, university lecturers in mathematics and engineering are often not trained in the non-traditional classroom methods. Some have argued that even if they included non-traditional teaching in their universities in fact they may not be in reality using the so called non-traditional methods and goals. They argue that lecturers are often lacking the underlying philosophical knowledge of the non-traditional goals and objectives, and therefore they are not in a position to implement such methodologies and assessment techniques, in reality, even when they say they are.

The non-traditional teaching and learning (NTTL) in mathematics and engineering needs to be well understood before any appropriate comparisons can be made with the older techniques if we are to do it in professional manner. For example the teachers of engineering courses need to reflect where the students are coming from, and where will they need to be after completing the course; also lecturers need to keep the context and goals of the course the degree program in mind while preparing for their class teaching content for the semester. So, we need to consider the knowledge, procedures, skills, beliefs and attitudes that will be expected for each student of mathematics or engineering at the end of the course that is to be taught in a time frame of 12 to 13 weeks; in addition to keeping the economic constraints of a university in modern times in check at all times.

The computer based teaching technology (e-learning) is now constantly used in mathematics and engineering courses. The e-learning methodology is considered to be in line with the non-traditional approaches than the traditional teaching approaches; and this paper critically reviews the literature on mathematics and engineering that have made comparisons of the approaches outlined. The paper will specifically examine the advantages/disadvantages of the approaches as well the manner in which they influence performance of students in mathematics and engineering courses.

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